Systems and methods for planning paths to guide robots

ABSTRACT

A computer-implemented method is provided for guiding a robot in a robotic system, by creating a refined path, based on an initial path in a three-dimensional space. The method includes receiving data related to creating the initial path, including a start point and an endpoint, and generating the initial path by interpolating the start point and the endpoint. The method also includes receiving inputs for at least one support point that defines a coordinate in the three-dimensional space for altering the initial path, and adjusting the initial path to generate the refined path by modifying a set of one or more polynomial functions, such that the refined path interpolates the at least one support point between the start point and the endpoint. The method further includes providing the refined path to a second computing module for guiding the robot.

CROSS REFERENCE TO RELATED APPLICATION

This application claims the benefit of and priority to U.S. ProvisionalPatent Application No. 62/352,384, filed Jun. 20, 2016, which is ownedby the assignee of the instant application and incorporated herein byreference in its entirety.

TECHNICAL FIELD

The present invention generally relates to computer-implemented methodsand apparatuses for automatic paths generation to guide robots in arobotic system.

BACKGROUND

Robotic path planning is used in a variety of industries to improvethroughput. For example, in a manufacturing processing facility, arobotic system can be used to automate processing (e.g., heating,cutting, gouging and marking) of workpieces by one or more thermalprocessing torches (e.g., plasma arc torches). Specifically, themanufacturing facility can include a computer numeric controller (CNC)used by an operator to input information specifying various operatingparameters. The CNC can be in electrical communication with one or morerobots of the manufacturing processing facility, where at least onerobot can have a thermal processing torch mounted thereon forautomatically processing a workpiece. In operation, a user can supplyinputs to the CNC to program the robot, such that the robot moves thethermal processing torch along a planned path to process the workpiece.This type of path planning can be used to create a transition betweentwo robotic operations or in a pick-n-place operation where processingstarts at a designated location.

Robotic path planning can be used in industrial manufacturingapplications, such as trimming, cutting (e.g., using laser, water-jet orplasma), 3D machining, de-burring, welding, dispensing, surfacing (e.g.,polishing, sanding or grinding), spraying (e.g., thermal projection,cold spray, coating or painting) and additive applications (e.g., 3Dprinting or material build-up). However, robotic path planning is notlimited to the manufacturing processing industry, as described above. Avariety of other industries also benefit from such planning. Forexample, robotic path planning can be used in the medical industry forrobotic assisted medical services, in the entertainment industry, inautomated warehousing for sorting, assembling, picking and/or placingapplications.

Generally, a robot is defined by a set of links, which are the solidstructural members of the robot, and a set of joints, which are themovable couplings between the joints. In addition, a tool center point(TCP) can be defined in relation to the robot or a tool mounted on therobot, where the TCP refers to the robot position, as well as the focalpoint of the tool if it is mounted on the robot (e.g., the tip of theplasma arc torch mounted to the robot). In the context of the presentinvention, a “path” of a robot refers to a path for moving the TCP froma start pose to an end pose. A “pose” refers to a set of position andorientation of the robot's TCP. In addition, in the context of thepresent invention, a “configuration change path” refers to a path forchanging the configuration of the robot, such as turning one or morejoints of the robot to reach a desired end configuration. Further, “ajoint-turn change path” refers to a path for turning a particular jointof the robot to reach a desired end joint-turn.

Typically, path planning for a robotic system is accomplished througheither a series of rapid moves of a robot executed in a joint space or aseries of feed moves of a robot executed in a Cartesian space. Inparticular, joint-space planning involves planning joint moves of arobot by specifying a set of joint parameters that describes theconfiguration of the robot. Joint-space planning does not requireverification of the path for robotic errors, such as singularity errorsor out-of reach errors. This type of planning naturally incorporatesconfiguration and joint-turn changes of the robot. However, planning injoint space typically results in an unintuitive movement of the robot inthe three-dimensional space. For example, in an exemplary planningprocess, the user simulates the joint moves of a robot between a startposture and an end posture. The user then verifies if the robot motionremains collision free. If not, the user adds a few via points betweenthe start and end postures to avoid collision. However, it is extremelydifficult to produce an accurate joint-space simulation of the robot,where the accuracy of the simulation depends on many factors, includingrobot parameters, robot loading and controller settings. For thesereasons, joint-space planning for a transition in tightthree-dimensional spaces is not feasible.

Cartesian-space planning involves planning a path of a robot byspecifying a set of feed moves in the Cartesian space between a startposture and an end posture. Although suitable for tight spaces, thisapproach requires configuration information and verification of the pathfor possible robotic and collosion errors.

Generally, path planning tools in today's market are either manualplanners or automated solvers. For manual planners, the user needs tocreate a series of transition points and meticulously ensure that theresulting path is efficient and error free (e.g., collision-free). Forexample, in both joint-space planning and Cartesian-space planning, theplacement of via points or feed moves in a three-dimensional environmentcan be made through a point-by-point manual teaching technique, whichrequires the user to move the robot to each via point between the startand end postures and save each via point. Upon completion, the path,which is defined by the start point, the via points and the end point,is tested to make sure that it is free of robotic or collision errors.If an error exits, some or all of the saved points are modified toremove the error. This is a repetitive process that is time consumingand challenging. Automated solvers typically use some type of heuristicsto drag the robot incrementally from the start point of the transitionto the desired target without planning the entire path as an initialstep. These automated approaches also do not allow a user to control orparticipate in the planning process, such as allowing the user to refinea path or perform other types of interactions. Further, in the contextof manufacturing processing, these tools are typically unable to designefficient paths in complex manufacturing facilities that have numerousworkpieces of varying geometries.

SUMMARY

It is therefore an objective of the present invention to provide agraphical tool that supports interactive path planning for guidingrobots in a robotic system, which can be useful in a variety ofapplications (e.g., manufacturing processing) where space is oftenconstrained. Using the graphical tool of the present invention, a usercan quickly specify an initial path in its entirety, which provides fastvisual feedback on possible errors as well as allows the user to quicklydetermine and specify other desired objectives for the path or for therobot itself (e.g., the robot arriving at the target location in adesired configuration). Such an automated, interactive approach to pathplanning reduces the effort required by a user to define a path, whilestill providing the user with a great degree of control over the pathdetails. The present invention thus simplifies path generation bycreating a user-interactive workflow that reduces planning time andimproves path accuracy. It is also an objective of the present inventionto provide systems and methods for automatically configuring a robot,such as automating joint-turn changes or configuration changes for therobot to enhance its operational capability. Therefore, advantages ofthe present invention include fast path planning, enabling planning forboth robot position and orientation, providing fast visual feedback ofpotential errors on the planned path, facilitating planning forconfiguration and joint turn changes for the robot, and accurate andinteractive control of robot positions and configurations.

In one aspect, a computer-implemented method is provided for guiding arobot in a robotic system, by creating a refined path, based on aninitial path in a three-dimensional space. The method includesreceiving, by a computing device, data related to creating the initialpath, including a start point and an endpoint and generating, by thecomputing device, the initial path by interpolating the start point andthe endpoint. Generating the initial path includes determining, by thecomputing device, a set of one or more polynomial functions to representthe initial path, where the set of one or more polynomial functionsdefines coordinates to model a route from the start point to the endpoint, and displaying, by the computing device on a graphical userinterface, the initial path. The method also includes receiving, by thecomputing device, inputs for at least one support point that defines acoordinate in the three-dimensional space for altering the initial path.The method further includes adjusting, by the computing device, theinitial path to generate the refined path by modifying the set of one ormore polynomial functions, such that the refined path interpolates theat least one support point between the start point and the endpoint. Inaddition, the method includes providing, by the computing device, therefined path to a second computing module for guiding the robot. In someembodiments, the computing device and the second computing module are inthe same robotic system.

In another aspect, a computer readable product, tangibly embodied on anon-transitory computer readable storage device, is provided for guidinga robot in a robotic system to move between a given start point and agiven endpoint, by designing a refined path based on an initial path ina three-dimensional space. The computer readable product includesinstructions operable to cause a computing device to receive datarelated to creating the initial path, including the start point and theendpoint, and generate the initial path by interpolating the start pointand the endpoint. Instructions operable to cause the computing device togenerate the initial path comprise instructions operable to cause thecomputing device to determine a set of one or more polynomial functionsto represent the initial path, where the set of one or more polynomialfunctions define coordinates to model a route from the start point tothe end point, and display the initial path on a graphical userinterface. The computer readable product also includes instructionsoperable to cause a computing device to receive inputs for at least onesupport point that defines a coordinate in the three-dimensional spacefor altering the initial path, and adjust the initial path to generatethe refined path by modifying the set of one or more polynomialfunctions, such that the refined path interpolates the at least onesupport point between the start point and the endpoint. The computerreadable product further includes instructions operable to cause acomputing device to provide the refined path an operating module forguiding the robot from the start point to the endpoint.

In yet another aspect, a computer-implemented robotic system is providedfor guiding a robotic means in a three-dimensional space. Themanufacturing processing system includes an input means for (i)receiving data related to creating an initial path, including a startpoint, an endpoint, and (ii) inputs for at least one support point thatdefines a coordinate in the three-dimensional space for altering theinitial path. The system also includes a determination means forgenerating the initial path by interpolating the start point and theendpoint. The determination means comprises a modeling means fordetermining a set of one or more polynomial functions to represent theinitial path, wherein the set of one or more polynomial functions definecoordinates to model a route from the start point to the end point, anda display means for causing to display on a graphical user interface theinitial path. The system further includes an adjusting means foradjusting the initial path to generate a refined path by modifying theset of one or more polynomial functions, such that the refined pathinterpolates the at least one support point between the start point andthe endpoint. The system additional includes an output means forproviding the refined path to a second computing module for guiding therobotic means from the start point to the endpoint.

In yet another aspect, a computer-implemented method is provided forguiding a robot having a tool mounted thereon for processing aworkpiece, by creating a refined path based on an initial path in athree-dimensional space. The method includes receiving, by a computingdevice, data related to creating the initial path, including a startpoint and an endpoint, and generating, by the computing device, theinitial path by interpolating the start point and the endpoint.Generating the initial path comprises determining, by the computingdevice, a set of one or more polynomial functions to represent theinitial path, where the set of one or more polynomial functions definescoordinates to model a route from the start point to the end point, anddetecting, by the computing device, a potential error associated withthe initial path. Generating the initial path also comprises displaying,by the computing device on a graphical user interface, the initial path,wherein at least one section of the initial path is configured tovisually indicate the potential error. The method additionally includesreceiving, by the computing device, data for at least one support pointthat defines a coordinate in the three-dimensional space for alteringthe initial path, and adjusting, by the computing device, the initialpath to generate the refined path by modifying the set of one or morepolynomial functions, such that the refined path interpolates the atleast one support point between the start point and the endpoint. Themethod further includes providing, by the computing device, the refinedpath to enable the robot and the tool to move substantially along therefined processing path to process the workpiece.

Any of the above aspects can include one or more of the followingfeatures. In some embodiments, at least one of the start point, theendpoint or the support point is user specifiable. In some embodiments,the set of one or more polynomial functions comprises at least oneBezier spline function.

In some embodiments, adjusting the initial path includes receiving userinput specifying a location of the support point in three dimensionalspace, adding at least one new polynomial function to the set of one ormore polynomial functions, such that the refined path includes the userspecified support point, the start point and the endpoint, anddisplaying the refined path on the graphical user interface. In someembodiments, the refined path comprises a plurality of segmentsconnected in series by the start point, the at least one support point,and the endpoint. Each segment is modeled by one polynomial function inthe set of one or more polynomial functions. In some embodiments, atleast one new polynomial function is added to the set of one or morepolynomial functions when a new support point is added.

In some embodiments, a control handle is established for each of thestart point, the endpoint and the support point. Each control handlepermits a user to change curvature of at least a portion of the initialpath or the refined path. In some embodiments, user input is received tomanipulate the control handle associated with at least one of the startpoint, the endpoint or the support point. In response, the set of one ormore polynomial functions is modified, such that at least a portion ofthe refined path has a modified curvature corresponding to themanipulated control handle, and the refined path is displayed on thegraphical user interface. In some embodiments, the at least portion ofthe refined path with the modified curvature comprises a path portionbetween the corresponding point for which the control handle is adjustedand an adjacent point.

In some embodiments, a potential error associated with at least one ofthe initial path or the refined path is detected, and at least a portionof the corresponding initial or refined path is color coded to visuallyindicate the potential error. The color-coded portion of thecorresponding path correlates to an area at which the potential error islikely to occur. The potential error can comprise the color-codedportion of the corresponding path being out of reach of the robot. Thepotential error can comprise the color-coded portion of thecorresponding path causing the robot to be in a singularityconfiguration. The potential error can comprise the robot colliding withan object in the robotic system if the robot attempts to reach thecolor-coded portion of the corresponding path. In some embodiments, atleast one of the initial path or the refined path is tessellated togenerate a plurality of tessellated points along the correspondinginitial or refined path; and each of the tessellated points along thecorresponding path is checked for the potential error.

In some embodiments, (i) a potential error associated with the refinedpath is detected. (ii) The refined path is displayed on the graphicaluser interface, where at least one section of the refined path is colorcoded to visually indicate the potential error associated therewith.(iii) Inputs are received for at least one modification of the refinedpath. (iv) The refined path is then adjusted by modifying the set of oneor more polynomial functions to model the modification to the refinedpath. Steps (i)-(iv) are repeated until no additional path modificationis received. In some embodiments, adjusting the refined path comprisesadding a new polynomial function to the set of one or more polynomialfunctions in response to receiving inputs to add a new support pointbetween the start and end points. In some embodiments, adjusting therefined path comprises modifying the set of one or more polynomialfunctions, such that at least a portion of the refined path has amodified curvature in response to receiving inputs to manipulate acontrol handle associated with at least one of the start point, theendpoint or the support point. In some embodiments, the refined path isdisplayed on the graphical user interface and a user is allowed toiteratively adjust the refined path via the graphical user interface bymanipulating a location of the at least one support point or a controlhandle of the at least one support point.

In some embodiments, the refined path enables the robot and a toolmounted on the robot to move substantially along the refined path toprocess a workpiece. In some embodiments, the robot is operated toenable a tool mounted thereon to cut a workpiece substantially along therefined path. In some embodiments, the tool comprises a cutting tool forcutting the workpiece. In some embodiments, the computing device learnsuser adjustments to the initial path to determine a pattern in theadjustments, and automatically generates a recommended path based on thelearning.

In some embodiments, inputs are received specifying a startconfiguration and an end configuration for moving one or more joints ofthe robot. A difference between the start and end configurations isdetected. A change path is added for moving the robotic joints from thestart configuration to the end configuration based on the difference,where the change path for moving the robotic joints avoids interferingwith the refined path. Automatically determining the change path cancomprise automatically locating a change point between the startconfiguration and the end configuration. The change path is adapted toinclude the start configuration, the change point, and the endconfiguration. In some embodiments, the change path is substantiallycollision free.

BRIEF DESCRIPTION OF THE DRAWINGS

The patent or application file contains at least one drawing executed incolor. Copies of this patent or patent application publication withcolor drawings will be provided by the Office upon request and paymentof the necessary fee.

The advantages of the invention described above, together with furtheradvantages, may be better understood by referring to the followingdescription taken in conjunction with the accompanying drawings. Thedrawings are not necessarily to scale, emphasis instead generally beingplaced upon illustrating the principles of the invention.

FIG. 1 is a block diagram of an exemplary robotic system, according toan illustrative embodiment of the present invention.

FIG. 2 is an exemplary approach for creating a desired path by a robotin the robotic system of FIG. 1, according to an illustrative embodimentof the present invention.

FIG. 3 illustrates an exemplary path modeled as a Bezier curve,according to an illustrative embodiment of the present invention.

FIG. 4 is a three-dimensional virtual environment in which an exemplarypath is displayed, according to one illustrative embodiment of thepresent invention.

FIG. 5 is an exemplary approach for determining and illustrating errorsassociated with a path for moving the robot of the robotic system ofFIG. 1, according to an illustrative embodiment of the presentinvention.

FIGS. 6a and 6b illustrate fine and course tessellations, respectively,of an exemplary curved path, according to illustrative embodiments ofthe present invention.

FIG. 7 is an exemplary path that is color coded to indicate potentialerrors, according to an illustrative embodiment of the presentinvention.

FIG. 8 is an exemplary approach for creating a refined path toincorporate a support point at a user-specified location, according toan illustrative embodiment of the present invention.

FIGS. 9a-9g is a set of exemplary paths depicting various adjustments auser can make to the paths, according to some illustrative embodimentsof the present invention.

FIGS. 10a-10e is another set of exemplary paths depicting variousadjustments a user can make to the paths, according to some illustrativeembodiments of the present invention.

FIG. 11 is an exemplary approach for changing a configuration or turninga joint of the robot of FIG. 1, according to an illustrative embodimentof the present invention.

FIG. 12 is an exemplary change path for changing the configuration ofthe robot of FIG. 1 from a start configuration to an end configuration,according to an illustrative embodiment of the present invention.

DETAILED DESCRIPTION

FIG. 1 is a block diagram of an exemplary robotic system 100 thatincludes a path planning processor 105, a user interface 110 and a robot115, according to an illustrative embodiment of the present invention.The user interface 110 can include a computer keyboard, mouse, agraphical user interface (e.g., a computerized display), other hapticinterfaces, voice input, or other input/output channels for a user tocommunicate with the path planning processor 105. In some embodiments,the graphical user interface of the user interface 110 is configured tovisualize a three-dimensional virtual environment in which one or morepaths generated by the processor 105 are mapped relative to variouscomponents of the manufacturing processing system 100. The path planningprocessor 105 is coupled to the robot 115 to automate or otherwisedirect the robot 115 to follow the planned path, such as for the purposeof processing (e.g., cutting) a workpiece using a tool (e.g., a plasmaarc torch) mounted on the robot 115. In some embodiments, the pathplanning processor 105 can also direct the robot 115 to change itsconfiguration or one or more specific joints along a desired changepath.

As shown in FIG. 1, the processor 105 includes a setup module 112, adetermination module 114, an adjustment module 116 and an implementationmodule 118. The modules 112-118 can be implemented in hardware only orin a combination of hardware and software to execute the path generationprocesses described below. In particular, the setup module 112 isconfigured to receive and process data from a user via the userinterface 110, including a start point and an endpoint for a desiredpath to move the TCP of the robot 115. The setup module 112 is alsoconfigured to receive inputs from the user to alter the resulting paths.In addition, the setup module 112 is configured to receive inputs fromthe user to specify changes to the configuration of the robot 115, suchas specifying an end configuration of the robot 115 that is differentfrom its start configuration. Further, the setup module 112 isconfigured to receive inputs from the user to specify changes to aparticular joint of the robot 115, such as specifying an end jointcoordinate of the robot 115 that is different from its start jointcoordinate. In general, the data provided to the user interface 110and/or processed by the setup module 112 can be in the form of anysuitable data structures, such as textual lists, XML documents, classobjects (e.g., instances of C++ or Java classes), other data structures,or any combination thereof.

The determination module 114 is configured to generate an initial pathfor moving the TCP of the robot 115 based on the parameters of the setupmodule 112. The determination module 114 is also adapted to plan aconfiguration change path or a joint-turn change path for changing theconfiguration or one or more joint turns of the robot 115, respectively,based on user inputs. The determination module 114 is further configuredto interact with the graphical user interface 110 to perform at leastone of: (i) visualize the initial path in a virtual environment relativeto other components of the robotic system 110, such as relative to therobot 115 and/or a workpiece, (ii) visualize the configuration changepath for changing the configuration of the robot 115 from a startposture to an end posture in the same virtual environment, or (iii)visualize the joint-turn change path for changing one or more jointturns of the robot 115 from a start joint coordinate to an end jointcoordinate in the same virtual environment. Such a display facilitatesuser interaction with the processor 105 to refine the initial pathand/or the configuration and joint-turn change paths.

The adjustment module 116 is configured to adjust the initial pathgenerated by the determination module 114 based on adjustment inputsreceived by the user interface 110 and processed by the setup module112. In some embodiments, the adjustment module 116 is also adapted toadjust the configuration and/or joint-turn change paths of the robot 115based on adjustment inputs received by the user interface 110 andprocessed by the setup module 112. The adjustment module 116 is furtherconfigured to interact with the graphical user interface 110 to causevisualization of the adjusted paths, thus encouraging further refinementfrom the user. In some embodiments, visualization of an adjusted pathincludes indication of one or more possible errors associated withcertain sections of the path.

The implementation module 118 can coordinate with the robot 115 suchthat the TCP of the robot 115 follows the refined path. Theimplementation module 118 can also manipulate the robot 115 to followthe configuration or joint-turn change path to implement changes to itsconfiguration or joint turn, respectively. In general, theimplementation module 118 can communicate with any one of the modules112-116 to obtain the pertinent information for articulating differentparts of the robot 115.

The system 100 further includes a memory 160 that is configured tocommunicate with one or more of the modules 112-118 of the processor105. For example, the memory 160 can be used to store data processed bythe setup module 112, one or more functions and values used by thedetermination module 114 to model the initial path, the configurationchange path or the joint-turn change path, one or more function andvalues used by the adjustment module 116 to alter the various paths,and/or instructions formulated by the implementation module 120 todirect the movement of the robot 115.

FIG. 2 is an exemplary approach 200 for creating a desired path formoving the robot 115 of the robotic system 100 of FIG. 1, according toan illustrative embodiment of the present invention. In the context ofthe present invention, a “path” refers to a planned route for moving thetool center point (TCP) of the robot 115 from a start pose to an endpose, where a “pose” refers to a set of position and orientation of therobot's TCP. As shown in FIG. 2, generating a desired path can includereceiving data related to creating an initial path (step 202),generating and displaying the initial path (step 204), determiningwhether user inputs are received for altering the initial path (step206), if so, adjusting the initial path based on the user-specifiedadjustment to generate and display a refined path (step 208),determining whether additional adjustments are received for iterativelyenhancing the refined path (step 210), and operating the robot 115substantially along the refined path if there is no additionaladjustment (step 212).

Optionally, the approach 200 is also configured to create/refine adesired change path for changing a configuration or a specific joint ofthe robot 115 during an iteration of path refinement (step 214). In thecontext of the present invention, a “configuration change path” refersto a planned route for changing the configuration of the robot 115, suchas turning one more joints of the robot to reach a desired end posture.Further, “a joint-turn change path” refers to a planned route forturning a particular joint of the robot to reach a desired joint endcoordinate. The change path can be used to suitably orient the robot 115(step 212).

At step 202, the setup module 112 of the processor 105 can process thedata for creating an initial path for moving the TCP of the robot 115,where the data is received from a user via the user interface 110. Thedata can include a start point and an endpoint of the path in athree-dimensional space. In some embodiments, the user can specify thestart and end points graphically via the user interface 110 within athree-dimensional virtual space.

At step 204, the determination module 114 is configured to generate theinitial path based on the data received at step 202, where the initialpath interpolates the start and end points. In some embodiments, thedetermination module 114 uses at least one (e.g., exactly one)three-dimensional polynomial function to represent the initial path as athree-dimensional spline, where the polynomial function defines a set ofthree-dimensional coordinates to model a route from the start point tothe endpoint. Generally, this spline can be based on any suitablepolynomial function(s). For example, a single cubic Bezier splinefunction with G2 (position and tangent) continuity can be used torepresent the initial spline path, where the Bezier spline function canbe decomposed into the following X, Y and Z components:B _(x)=(1−t)³ P _(0x)+3(1−t)² tP _(1x)+3(1−t)t ² P _(2x) +t ³ P_(3x)  Equation 1B _(y)=(1−t)³ P _(0y)+3(1−t)² tP _(1y)+3(1−t)t ² P _(2y) +t ³ P_(3y)  Equation 2B _(z)=(1−t)³ P _(0z)+3(1−t)² tP _(1z)+3(1−t)t ² P _(2z) +t ³ P_(3z)  Equation 3In Equations 1-3, B_(x), B_(y) and B_(z) represent X, Y and Zcoordinates of a Bezier curve at each instant of parameter t, where t isadapted to change from 0 to 1. P₀ and P₃ represent the start and endpoints of the Bezier curve. P₁ and P₂ represent control handles of theBezier curve at the start and end points, respectively. In someembodiments, the control handles P₁ and P₂ are user adjustable to enablethe user to change the shape of the Bezier curve between the start andend points P₀ and P₃, such as changing the curvature and/or the tangentof the curve. FIG. 3 illustrates an exemplary path (e.g., an initialpath) modeled as a Bezier curve, according to an illustrative embodimentof the present invention.

In some embodiments, the determination module 114 can interact with theuser interface 110 to display the initial path in a three-dimensionalvirtual environment. FIG. 4 shows a three-dimensional virtualenvironment in which an exemplary path, e.g., an initial path 400, isdisplayed, according to one illustrative embodiment of the presentinvention. As shown, the virtual environment depicts the robot 115, aworkpiece 402, and the initial path 400, which is generated by thedetermination module 114 at step 204 to guide the robot 115 to processthe workpiece 402. The initial path 400 includes the user-specifiedstart point 404, the user-specified end point 406, and acomputer-generated curve that connects these two points, where the curvecan be defined by a three-dimensional Bezier spline function, asdescribed above. In some embodiments, an end effector 410 of the robot115 has a processing tool 408, such as a plasma arc torch, mountedthereon for processing (e.g., cutting) the workpiece 402 along the path400.

In some embodiments, displaying the initial path at step 204 alsoincludes visually illustrating one or more errors associated with thispath. FIG. 5 is an exemplary approach 500 for determining andillustrating errors associated with a given path for moving the robot115 of the robotic system 100 of FIG. 1, according to an illustrativeembodiment of the present invention. At step 502, for a given path, thedetermination module 114 tessellates the path to return a list oftessellated points. Tessellating a path, such as a Bezier curve,involves determining a plurality of spaced points on the path which canbe used to approximate the original Bezier curve if straight lines areused to connect these points. In some embodiments, closeness between aBezier curve and a line created by two neighboring tessellated points onthe curve are defined by three parameters: (i) a chordal deviationbetween the line and the Bezier curve, (ii) a length of the line and(iii) an angle between two consecutive lines. In some embodiments,thresholds for one or more of the chordal deviation, the length of aline between each pair of adjacent tessellated point, and the anglebetween two consecutive lines are user specified. Thus, the lower thethreshold value for each parameter, the finer the tessellation and thegreater the number of tessellated points generated. FIGS. 6a and 6billustrate fine and course tessellations, respectively, of an exemplarycurved path, according to illustrative embodiments of the presentinvention.

At step 504, the determination module 114 solves inverse kinematicsbased on one or more kinematics equations to determine the jointparameters of the robot 115 in order to reach each of the tessellatedpoints on the given path from step 502. At step 506, the determinationmodule 114 uses the joint parameters corresponding to each tessellatedpoint to check for one or more potential errors associated with thatpoint. One potential error comprises the tessellated point on the givenpath being out of reach by the robot 115. Another potential errorcomprises the tessellated point on the given path causing the robot 115to be in a singularity posture, such as when the robot loses its abilityto move its end effector 410 (shown in FIG. 4) in some direction nomatter how it moves its joints or when the robot has infinite jointposture possibilities to reach the next Cartesian posture. Yet, anotherpotential error comprises the robot 115 colliding with another object ofthe robotic system if the robot 115 attempts to reach the tessellatedpoint, such as colliding with the workpiece 402 of FIG. 4 or anotheradjacent object (not shown).

At step 508, the determination module 114 can color code one or moresections of a given path to visually indicate the potential errorsdetected from step 506. Specifically, for the tessellated points thatare associated with a certain type of error (e.g., singularity,collision and/or out-of-reach), the points are displayed in a specificcolor, along with segments of the path connecting these points. Forexample, an affected path segment associated with (i) a singularityerror can be coded red, (ii) a collision error can be coded dark red and(iii) an out-of-reach error can be coded blue. In some embodiments,another color (e.g., white) can be assigned to points and theirinterconnecting path segments that are error free. Such color-coded pathdisplay provides visual feedback to the user regarding the planned pathand allows the user to quickly adjust the path to remove the errors, asexplained below. FIG. 7 is an exemplary path that is color coded toindicate potential errors, according to an illustrative embodiment ofthe present invention. As shown, the dark red path section 602 indicatesa potential collision error, where it is determined that the robot 115is likely to collide with another object if the robot 115 attempts toreach that path section 602. In addition, the blue path section 604 ofthe same path indicates a potential out-of-reach error, where the robot115 is unlikely to be able to reach that path section 604.

Referring back to the path-generation approach 200 of FIG. 2, asdescribed above, at step 204 the determination module 114 is adapted togenerate an initial path and display the initial path to the user viathe user interface 110, where the initial path can be color coded toindicate areas of potential errors. At step 206, in response to thedisplayed initial path, the user can provide inputs to adjust theinitial path to eliminate these potential errors or otherwise fine tunethe initial path. The adjustment inputs can be received by theadjustment module 116 via the user interface 110, such as graphically inthe same three-dimensional virtual environment in which the initial pathis displayed. If not adjustment inputs are received, the process 200 isconfigured to execute step 212 by directing the implementation module118 to operate the robot 115 substantially along the initial path.

If adjustment inputs are received at step 206, the adjustment module 116is adapted to adjust the initial path at step 208, thereby generating arefined path based on the user inputs. The adjustment module 116 is alsoconfigured to interact with the user interface 110 to graphicallyillustrate the refined path, such as in the same virtual environmentwhere the initial path was illustrated. For example, the graphical userinterface 110 can illustrate the movement of the user when adjusting theinitial path (e.g., the user moving a support point or control handle asdescribed in detail below), and provide immediate visual feedback of theadjusted path. In some embodiments, the adjustment module 116 executesthe error-checking process 500 of FIG. 5 with respect to the refinedpath to visually illustrate one or more errors (e.g., singularity,collision and/or out-of-reach errors) associated with the refined path.Such a display encourages the user to further refine the path to corrector otherwise optimize the path. Further, in some embodiments, theadjustment module 116, in cooperation with the user interface 110, isconfigured to illustrate the orientation of the TCP of the robot 115along a refined path to visually demonstrate how the TCP of the robot115 can follow the path. The orientation of the TCP of the robot 115 canbe determined by interpolating the orientations of the TCP between twoconsecutive support points. In some embodiments, when the path includesone or more support points in the middle of the path, the orientation ofthe TCP of the robot 115 at that support point is adjustable by theuser.

In some embodiments, the inputs for adjusting the initial path receivedat step 206 comprise data that specifies at least one support pointalong the initial path and data for moving the support point to adifferent location in the three-dimensional space. In response, theadjustment module 116 at step 208 is adapted to alter the initial pathsuch that a refined path is generated to interpolate the relocatedsupport point between the start and end points of the initial path.

FIG. 8 is an exemplary approach 800 for generating a refined path toincorporate a support point at a user-specified location, according toan illustrative embodiment of the present invention. At step 802, theadjustment module 116 determines the coordinate of the user-specifiedsupport point, where the support point is on the initial path prior tothe user moving it for the purpose of altering the initial path. Forexample, as shown in FIG. 4, the user can specify a support point 412 onthe initial path 400. This support point is movable by the user, therebyallowing the user to adjust the path. In some embodiments, the supportpoint is associated with a control handle 413, which allows the user toadjust the tangent and/or curvature of the adjacent segments connectedto the support point 412. The control handle 413 shared by the twoadjacent segments assures that refinement to the initial path 400preserves certain continuity conditions for the path, such as G2(position and tangent) continuity of the path. Generally, the term“support point” refers to the meeting point of two segments (e.g.,Bezier curves) in a path (e.g, a Bezier spline curve). Two neighboringsegments on a path share a single support point and correspondingcontrol handle.

At step 804, the adjustment module 116 calculates one or more parametersassociate with the support point, such as the tangent value of theinitial path at the support point. At step 806, the adjustment module116 splits the initial path into two segments at the support point,where each segment is modeled by a new polynomial function.Specifically, a first segment has (i) the same start point and the sametangent at the start point as the initial path and (ii) an end pointthat is the support point and the tangent at the end point is the sameas the tangent of the initial path at the support point. A secondsegment has (i) a start point that is the support point and the tangentat the start point is the same as the tangent of the initial path at thesupport point and (ii) the same end point and the same tangent at theend point as the initial path.

At step 808, the adjustment module 116 detects whether the user hasdragged/moved the support point on the initial path to a new location.If that is the case, at step 810, the adjustment module 116 adjusts theinitial path such that the refined path interpolates the support pointat the new location between the start and end points of the initialpath. This means that the two polynomial functions generated from step806 are suitably modified so that the endpoint of the first segment andthe start point of the second segment are both at the new support pointlocation. However, if the support point is not moved to a new location,the adjustment module 116 takes no further action for adjusting the pathand control reverts back to step 210 of FIG. 2. Thus, when a new supportpoint is added, the original polynomial function corresponding to thesection of the path on which the new support point is located isreplaced with two new polynomial functions to represent the splitting ofthe path section, and the two polynomial functions can be modified toreflect any movement of the support point to alter the path.

In some embodiments, the two segments corresponding to the new supportpoint in the refined path are Bezier spline functions. These neighboringBezier spline functions are constrained to have a G2 (position andtangent) continuity in the spline. To ensure that the curve of therefined path is G1 (position-wise) continuous, the segments of therefined path are connected by the support points. To ensure that thecurve of the refined path is G2 (tangent-wise) continuous, the controlhandles of the neighboring segments at the point of connection (i.e.,the shared support point) have the same slope.

Referring back to the path-generation approach 200 of FIG. 2, at steps206 and 208, another path adjustment involves the user changing thecurvature and/or tangent of one or more sections of a path. This can beaccomplished by the user adjusting (e.g., moving) a control handleassociated with each support point as well as associated with each ofthe start and end points. In some embodiments, the start and end pointsare treated as specialized support points that are fixed in space (i.e.not movable by a user). By moving a control handle of a support point, acontrol handle of a start point or a control handle of an end point, theuser can alter the curvature and/or tangent of at least a portion of apath, such as neighboring segment(s) connected to the support point.Adjusting a control handle of a support point is adapted to modify thecorresponding polynomial function used to model the section of the pathbeing adjusted (e.g., the section of the path connected between thecorresponding support point for which the control handle is adjusted andan adjacent support point) so as to reflect the change incurvature/tangent to the path section. This typically does notnecessitate adding a new polynomial function to the set of functionsused to represent the processing path.

At step 210, the user can iteratively adjust the refined path byspecifying additional adjustments at each iteration. During eachiteration, the refined path can be graphically displayed to the user viathe user interface 110 to encourage further fine tuning from the useruntil a desired path is created. For example, the refined path createdat each adjustment iteration can be evaluated for certain errors (e.g.,singularity, collision and/or out-of-reach errors) using theerror-checking routine 500 of FIG. 5 and the errors can be color-codedrelative to the refined path to provide visual feedback to the user forthe purpose of facilitating further adjustment. As described above, theadjustment at each iteration can involve one of (i) adding a supportpoint on the path from the previous iteration and changing the locationof the support point, (ii) deleting a support point, (iii) adjusting acontrol handle associated with one of the support point(s), start pointor endpoint of the path from the previous iteration, and/or (iv)changing one or more of the tessellation parameters.

In some embodiments, the initial path is represented by a single curvebetween a start point and an endpoint, where the curve is modeled by asingle three-dimensional polynomial function. At the subsequentiterations, an additional three-dimensional polynomial function is addedto the function set for each additional support point specified betweenthe start and end points, where each of the polynomial functions in thefunction set represents a path segment between two support points. Thus,if a refined path includes one or more support points, the path isrepresented by multiple segments connected in series by the start point,the support point(s), and the endpoint. In some embodiments,manipulating a control handle does not involve adding or deleting afunction relative to the function set, but requires modification of atleast one of the existing functions in the function set.

FIGS. 9a-9g is a set of exemplary paths depicting various adjustments auser can make to the paths, according to some illustrative embodimentsof the present invention. FIG. 9a shows an initial path 900 that can bemodeled by a single three-dimensional polynomial function, such as afunction with the X, Y, Z components of Equations 1-3. The initial path900 can be a Bezier curve having a user-specified start point 902 and auser-specified endpoint 904. In FIG. 9b , a user can select (e.g., clickon) either one of the start point 902 or the end point 904 of theinitial path 900, which prompts a control handle 906 associated with theselected point (e.g., the end point 904) to appear. In FIG. 9c , theuser can adjust the control handle 906 corresponding to the end point904, such as rotating or moving the control handle 906, to adjust thecurvature and/or tangent of the initial path 900. As shown, the user candrag the control handle 906 in a specific direction 908 in thethree-dimensional space, in which case the resulting refined path 910becomes curved towards that direction 908. In some embodiments,adjusting the control handle 906 modifies the corresponding polynomialfunction used to model the section of the path being adjusted so as toreflect the change in curvature/tangent, but does not add a newpolynomial function to the set of functions used to represent the path910. Thus, the refine path 910 can still be represented by a singlethree-dimensional polynomial function, but modified to reflect thechanged curvature/tangent.

Furthermore, as shown in FIG. 9d , the user can further adjust therefined path 910 by introducing a support point 912 on the path 910between the start point 902 and the endpoint 904, which are both fixed.For example, the user can introduce the support point 912 by doubleclicking on a location of the path 910 between the start and end point902, 904. Once the support point 912 appears, the path 910 is split intotwo segments 914 a, 914 b and the original polynomial function used torepresent the path 910 is replaced with two new polynomial functionsrepresenting the two segments 914 a, 914 b. As shown, segment 914 aextends from the start point 902 to the support point 912 and segment914 b extends from the support point 912 to the endpoint 904. As shownin FIG. 9e , the user can move the support point 912 to modify the path910 such that the resulting path 914 interpolates the relocated supportpoint 912 between the start and end point 902, 904. In some embodiments,this adjustment triggers modification of the two polynomial functionsrepresenting the segments 914 a, 914 b such that these segments areconnected at the relocated support point 912 and satisfy certaincontinuity constraints. As shown in FIG. 9f , the resulting refined path914 can be further modified by the user by adjusting the control handle916 associated with the support 912, which changes the curvature of thepath 914 to generate a further refined path 918. Other modificationsinclude adding one or more support points (not shown) and/or removingone or more support points. For example, as shown in FIG. 9g , the usercan remove the support point 912 by right clicking on the support point912, in which case the support point is deleted and the path 918 isreturned to a state where only one polynomial function is used torepresent the path 918 since there is no support point between the startand end points 902, 904.

FIGS. 10a-10e is another set of exemplary paths depicting variousadjustments a user can make to the paths relative to a workpiece 1000,according to some illustrative embodiments of the present invention.FIG. 10a shows an exemplary initial path 1002 connected by a straightBezier curve between a start point 1004 and an end point 1006. FIG. 10bshows a support point 1008 being added by a user at a desired positionalong the initial path 1002. FIG. 10c shows the support point 1008 beingmoved by a user to a different location in space. In response, theadjustment module 116 is configured to modify the initial path 1002 togenerate a refined path 1010 such that the refined path 1010 includesthe relocated support point 1008. FIG. 10d shows the control hand 1012of the support point 1008 being adjusted by the user. In response, theadjustment module 116 is configured to modify the refined path 1010 togenerate another refined path 1014 such that it includes an adjustedcurvature corresponding to the modified control handle 1012. FIG. 10eshows one or more tessellated points 1016 on the refined path 1010,which can be used to detect errors associated with the path 1010 asdescribed above. Each support point on the initial path or the refinedpath holds information for the position and orientation of the TCP ofthe robot 115. This means that when the TCP of the robot 115 is passingthat support point, the TCP will have that corresponding position andorientation. To have a path with complete information, each tessellatedpoint on the path should also hold the information of the position andorientation of the TCP of the robot 115. The position interpolation ofthe tessellation points depends on the tessellation parameters describedabove (e.g., distance, chordal deviation and angle parameters). When theposition of the tessellated points is defined, the orientation of thetessellated points is added based on the length of the curve between twoconsecutive points over the total length of the curve between twoconsecutive support points multiplied by the orientation change requiredto move from the orientation of the first support point of that curve tothe orientation of the next support point plus the orientation of thefirst tessellated point of the two consecutive tessellated points. Theorientation of the added support points (i.e. not the start supportpoint and end support point) can be adjusted by the user. Adjustments tothe support point orientation changes the orientation of the tessellatedpoints on the curve segments before and after the support point.

Referring back to the path-generation approach 200 of FIG. 2, in someembodiments, at each adjustment iteration represented by steps 208 and210, the process 200 also includes the optional step 214 of generating achange path for reconfiguring the robot 115 or turning a joint of therobot 115 based on user input. FIG. 11 is an exemplary approach 1100 forchanging the configuration or turning a joint of the robot 115 of FIG.1, according to an illustrative embodiment of the present invention.

As shown, at step 1102, data is received from a user, such as via theuser interface 110, to specify a robot configuration change or ajoint-turn change. Data related to a configuration change includes astart configuration of the robot 115 at the start point of the path(i.e., the robot's TCP path) and/or an end configuration of the robot115 at the end point of the path, where the start and end configurationsare different from each other. Data related to a joint turn changeincludes a start coordinate of a particular joint of the robot 115 atthe start point of the path (i.e., the robot's TCP path) and/or an endcoordinate of the joint at the endpoint of the path, where the start andend coordinates of the joint are in different turns from each other. Atstep 1104, the determination module 114 determines whether aconfiguration change or a joint-turn change is required for the robot115 based on the user input. A configuration change involves detecting adifference between the start configuration and the end configuration ofthe robot 115. A joint-turn change involves detecting a change betweenthe start coordinate and the end coordinate for the joint of the robot115.

If a change is detected, the determination module 114 automaticallygenerates a change path at steps 1106 and 1108. In the case of aconfiguration change, the change path specifies a path for moving one ormore joints of the robot 115 to accomplish the change from the start toend configuration. In the case of a joint-turn change, the change pathspecifies a route for moving the user-specified joint of the robot 115to accomplish the joint turn from the start joint coordinate to the endjoint coordinate. Specifically, for generating the change path inrelation to the configuration change, the determination module 114 atstep 1106 automatically determines one or more change points that arereachable by the robot 115 in either the start or end configuration.Then, at step 1108, the determination module 114 determines a set ofjoint movements required to change the configuration at the changepoint. The resulting change path thus includes the start configurationof the robot 115 corresponding to the start point of the path, the pathon which the TCP of the robot 115 moves during configuration change, andthe end configuration of the robot 115 corresponding to the end point ofthe path. For generating the change path in relation to the joint-turnchange, the determination module 114 at step 1106 automaticallydetermines one or more change points that are reachable by the robot 115in either the start joint coordinate or the end joint coordinate. Then,at step 1108, the determination module 114 determines a movement of thespecific joint required to reach that change point. The resulting changepath thus includes the start joint coordinate corresponding to the startpoint of the path, the path on which the TCP of the robot 115 movesduring joint turn change, and the end joint coordinate correspond to theend point of the path. Control reverts back to step 210 of the process200 at the conclusion of the change path routine 1100.

In some embodiments, the change path for moving the robot 115 thatimplements either a configuration change or a joint-turn change issubstantially independent of the refined path for moving the tool centerpoint (TCP) of the robot 115 and does not interfere with the refinedpath. In some embodiments, the determination module 114 generates thechange path to be substantially error free, such as free of collision.In some embodiments, the change path is user adjustable such that a usercan fine tune the path to implement the configuration change or thejoint-turn change desired. In some embodiments, the determination module114, in cooperation with the user interface 110, is configured todisplay within a virtual space a change path for changing theconfiguration of the robot 115 or turning a joint of the robot 115.

FIG. 12 is an exemplary change path 1200 for changing the configurationof the robot 115 of FIG. 1 from a start configuration to an endconfiguration, according to an illustrative embodiment of the presentinvention. The robot 115 can assume a start configuration at the changepoint 1202 and change its configuration along the change path 1200 suchthat it ends with an end configuration again at the change point 1202.The robots 115 can then continue on a refined path 1204 with the new endconfiguration to, for example, process the workpiece 1204. Generally,the configuration change or joint-turn change of the robot 115 can occurbefore or after the robot 115 moves to follow a refined path in relationto its TCP.

Referring back to the path-generation approach 200 of FIG. 2, at step212, once the user if satisfied with the planned path, theimplementation module 118 is configured to direct the robot 115 suchthat the TCP of the robot 115 follows the refined path generated. Theimplementation module 118 can directly interact with the robot 115 toguide the robot 115. Alternatively, the implementation module 118 caninteract with the robot 115 indirectly via one or more intermediatecomputing modules, where the implementation module 118 and theintermediate module(s) can be in the same robotic system 100. In someembodiments, the planned path generated by the process 200 can be usedto guide the robot 115 to enable a tool (e.g., a plasma arc torch)mounted to the end effector of the torch to cut a workpiecesubstantially along the path, such as the setup shown the processingenvironment of FIG. 4. In some embodiments, the implementation module118 can also change the configuration of the robot 115 or turn a jointof the robot 115 based on a change path generated by the process 200. Insome embodiments, the robot 115 is guided along the refined path and/orthe change path to perform at least one of trimming, cutting (e.g.,using laser, water-jet or plasma), 3D machining, de-burring, welding,dispensing, surfacing (e.g., polishing, sanding, or grinding), spraying(e.g., thermal projection, cold spray, coating, or painting) or additiveapplications (e.g., 3D printing or material build-up).

In some embodiments, the path planning process can be fully automatedwithout user adjustment. In such a case, the user only needs to specifythe start point and the end point of the path. The processor 105 is ableto automatically determine a recommended path by learning fromhistorical user adjustments. Thus, the recommended path by the processor105 is able to capture patterns in user preference.

It should be understood that various aspects and embodiments of theinvention can be combined in various ways. Based on the teachings ofthis specification, a person of ordinary skill in the art can readilydetermine how to combine these various embodiments. Modifications mayalso occur to those skilled in the art upon reading the specification.

What is claimed is:
 1. A computer-implemented method for guiding a robotin a robotic system, by creating a refined path, based on an initialpath in a three-dimensional space, the method comprising: receiving, bya computing device, data related to creating the initial path, includinga start point and an endpoint; generating, by the computing device, theinitial path by interpolating the start point and the endpoint, whereingenerating the initial path comprises: determining, by the computingdevice, a set of one or more polynomial functions to represent theinitial path, wherein the set of one or more polynomial functionsdefines coordinates to model a route from the start point to the endpoint; and displaying, by the computing device on a computerizeddisplay, the initial path in a virtual environment; receiving, by thecomputing device, inputs for at least one support point on the initialpath that defines a coordinate in the three-dimensional space foraltering the initial path; causing a control handle to appear on thecomputerized display for at least one of the start point, the endpointor the support point, the control handle permitting a user to rotate ormove the control handle in the three-dimensional space to changecurvature of at least a portion of the initial path or the refined path;adjusting, by the computing device, the initial path to generate therefined path by modifying the set of one or more polynomial functions,such that the refined path interpolates the at least one support pointbetween the start point and the endpoint; and providing, by thecomputing device, the refined path to a second computing module forguiding the robot.
 2. The computer implemented method of claim 1,wherein at least one of the start point, the endpoint or the supportpoint is user specifiable.
 3. The computer implemented method of claim2, wherein adjusting the initial path comprises: receiving user inputspecifying a location of the support point in three dimensional space;adding at least one new polynomial function to the set of one or morepolynomial functions, such that the refined path includes the userspecified support point, the start point and the endpoint; anddisplaying the refined path on the graphical user interface.
 4. Thecomputer implemented method of claim 1, further comprising: receivinguser input to manipulate the control handle associated with at least oneof the start point, the endpoint or the support point, modifying the setof one or more polynomial functions, such that at least a portion of therefined path has a modified curvature corresponding to the manipulatedcontrol handle; and displaying the refined path on the graphical userinterface.
 5. The computer implemented method of claim 4, wherein the atleast portion of the refined path with the modified curvature comprisesa path portion between the corresponding point for which the controlhandle is adjusted and an adjacent point.
 6. The computer implementedmethod of claim 1, wherein the refined path comprises a plurality ofsegments connected in series by the start point, the at least onesupport point, and the endpoint, wherein each segment is modeled by onepolynomial function in the set of one or more polynomial functions. 7.The computer implemented method of claim 6, further comprising adding atleast one new polynomial function to the set of one or more polynomialfunctions when a new support point is added.
 8. The computer implementedmethod of claim 1, wherein the set of one or more polynomial functionscomprises at least one Bezier spline function.
 9. The computerimplemented method of claim 1, further comprising: detecting a potentialerror associated with at least one of the initial path or the refinedpath; and color coding at least a portion of the corresponding initialor refined path to visually indicate the potential error, thecolor-coded portion of the corresponding path correlates to an area atwhich the potential error is likely to occur.
 10. The computerimplemented method of claim 9, wherein the potential error comprises thecolor-coded portion of the corresponding path being out of reach of therobot.
 11. The computer implemented method of claim 9, wherein thepotential error comprises the color-coded portion of the correspondingpath causing the robot to be in a singularity configuration.
 12. Thecomputer implemented method of claim 9, wherein the potential errorcomprises the robot colliding with an object in the robotic system ifthe robot attempts to reach the color-coded portion of the correspondingpath.
 13. The computer implemented method of claim 9, furthercomprising: tessellating at least one of the initial path or the refinedpath to generate a plurality of tessellated points along thecorresponding initial or refined path; and checking at each of thetessellated points along the corresponding path for the potential error.14. The computer implemented method of claim 1, further comprisingoperating the robot to enable a tool mounted thereon to cut a workpiecesubstantially along the refined path, wherein the tool comprises acutting tool for cutting the workpiece.
 15. The computer implementedmethod of claim 1, further comprising: learning, by the computingdevice, user adjustments to the initial path to determine a pattern inthe adjustments; and automatically generating, by the computing device,a recommended path based on the learning.
 16. The computer implementedmethod of claim 1, further comprising: receiving, by the computingdevice, inputs specifying a start configuration and an end configurationfor moving one or more joints of the robot; automatically determining,by the computing device, a difference between the start and endconfigurations; adding a change path for moving the robotic joints fromthe start configuration to the end configuration based on thedifference, wherein the change path for moving the robotic joints avoidsinterfering with the refined path.
 17. The computer implemented methodof claim 16, wherein automatically determining the change path comprisesautomatically locating, by the computing device, a change point betweenthe start configuration and the end configuration, wherein the changepath is adapted to include the start configuration, the change point,and the end configuration.
 18. The computer implemented method of claim16, wherein the change path is substantially collision free.
 19. Thecomputer implemented method of claim 1, further comprising: displayingthe refined path on the graphical user interface; and allowing a user toiteratively adjust the refined path via the graphical user interface bymanipulating a location of the at least one support point or a controlhandle of the at least one support point.
 20. The computer implementedmethod of claim 1, wherein the computing device and the second computingmodule are in the same robotic system.
 21. A non-transitory computerreadable storage medium having stored thereon a computer program productfor guiding a robot in a robotic system to move between a given startpoint and a given endpoint, by designing a refined path based on aninitial path in a three-dimensional space, the computer program productincluding computer-executable instructions adapted to be executed on acomputing device to implement a method comprising: receive data relatedto creating the initial path, including the start point and theendpoint; generate the initial path by interpolating the start point andthe endpoint, wherein instructions operable to cause the computingdevice to generate the initial path comprises instructions operable tocause the computing device to: determine a set of one or more polynomialfunctions to represent the initial path, wherein the set of one or morepolynomial functions define coordinates to model a route from the startpoint to the end point; and display the initial path on a computerizeddisplay; receive inputs for at least one support point on the initialpath that defines a coordinate in the three-dimensional space foraltering the initial path; cause a control handle to appear on thecomputerized display for at least one of the start point, the endpointor the support point, the control handle permitting a user to rotate ormove the control handle in the three-dimensional space to changecurvature of at least a portion of the initial path or the refined path;adjust the initial path to generate the refined path by modifying theset of one or more polynomial functions, such that the refined pathinterpolates the at least one support point between the start point andthe endpoint; and provide the refined path an operating module forguiding the robot from the start point to the endpoint.
 22. The computerreadable product of claim 21, wherein the computer readable productincludes instructions operable to further cause the computing device toprovide the refined path to enable the robot and a tool mounted on therobot to move substantially along the refined path to process aworkpiece.
 23. The computer readable product of claim 22, wherein thetool comprises a cutting tool for cutting the workpiece.
 24. Acomputer-implemented robotic system of a manufacturing processing systemfor guiding a robotic means in a three-dimensional space, thecomputer-implemented robotic system comprising: an input means for (i)receiving data related to creating an initial path, including a startpoint, an endpoint, and (ii) inputs for at least one support point thatdefines a coordinate in the three-dimensional space for altering theinitial path; a determination means for generating the initial path byinterpolating the start point and the endpoint, the determination meanscomprises: a modeling means for determining a set of one or morepolynomial functions to represent the initial path, wherein the set ofone or more polynomial functions define coordinates to model a routefrom the start point to the end point; and a display means for causingto display on a computerized display the initial path in a virtualenvironment; a prompting means for causing a control handle to appear onthe computerized display for at least one of the start point, theendpoint or the support point, the control handle permitting a user torotate or move the control handle in the three-dimensional space tochange curvature of at least a portion of the initial path or therefined path; an adjusting means for adjusting the initial path togenerate a refined path by modifying the set of one or more polynomialfunctions, such that the refined path interpolates the at least onesupport point between the start point and the endpoint; and an outputmeans for providing the refined path to a second computing module forguiding the robotic means from the start point to the endpoint.
 25. Thecomputer-implemented robotic system of claim 24, further comprising anenabling means for causing the robot and a tool mounted on the robot tomove substantially along the refined processing path to process aworkpiece.
 26. The computer-implemented robotic system of claim 25,wherein the tool comprises a cutting tool for cutting the workpiece. 27.A computer-implemented method for guiding a robot having a tool mountedthereon for processing a workpiece, by creating a refined path based onan initial path in a three-dimensional space, the method comprising:receiving, by a computing device, data related to creating the initialpath, including a start point and an endpoint; generating, by thecomputing device, the initial path by interpolating the start point andthe endpoint, wherein generating the initial path comprises:determining, by the computing device, a set of one or more polynomialfunctions to represent the initial path, wherein the set of one or morepolynomial functions defines coordinates to model a route from the startpoint to the end point; detecting, by the computing device, a potentialerror associated with the initial path; and displaying, by the computingdevice on a computerized display, the initial path in a virtualenvironment, wherein at least one section of the initial path isconfigured to visually indicate the potential error; receiving, by thecomputing device, data for at least one support point on the initialpath that defines a coordinate in the three-dimensional space foraltering the initial path; causing a control handle to appear on thecomputerized display for at least one of the start point, the endpointor the support point, the control handle permitting a user to rotate ormove the control handle in the three-dimensional space to changecurvature of at least a portion of the initial path or the refined path;adjusting, by the computing device, the initial path to generate therefined path by modifying the set of one or more polynomial functions,such that the refined path interpolates the at least one support pointbetween the start point and the endpoint; and providing, by thecomputing device, the refined path to enable the robot and the tool tomove substantially along the refined processing path to process theworkpiece.
 28. The computer implemented method of claim 27, furthercomprising: (i) detecting a potential error associated with the refinedpath; (ii) displaying, on the graphical user interface, the refinedpath, wherein at least one section of the refined path is color coded tovisually indicate the potential error associated therewith; (iii)receiving inputs for at least one modification of the refined path; (iv)adjusting the refined path by modifying the set of one or morepolynomial functions to model the modification to the refined path; and(v) repeating steps (i)-(iv) until no additional path modification isreceived.
 29. The computer implemented method of claim 28, wherein thepotential error comprises the color-coded portion of the correspondingpath being out of reach of the robot.
 30. The computer implementedmethod of claim 28, wherein the potential error comprises thecolor-coded portion of the corresponding path causing the robot to be ina singularity configuration.
 31. The computer implemented method ofclaim 28, wherein the potential error comprises the robot colliding withan object in the robotic system if the robot attempts to reach thecolor-coded portion of the corresponding path.
 32. The computerimplemented method of claim 28, wherein adjusting the refined pathcomprises adding a new polynomial function to the set of one or morepolynomial functions in response to receiving inputs to add a newsupport point between the start and end points.
 33. The computerimplemented method of claim 28, wherein adjusting the refined pathcomprises modifying the set of one or more polynomial functions, suchthat at least a portion of the refined path has a modified curvature inresponse to receiving inputs to manipulate a control handle associatedwith at least one of the start point, the endpoint or the support point.34. The computer implemented method of claim 27, further comprising:receiving, by the computing device, inputs specifying a startconfiguration and an end configuration for moving one or more joints ofthe robot; automatically determining, by the computing device, adifference between the start and end configurations; adding a changepath to the refined path for moving the robotic joints from the startconfiguration to the end configuration based on the difference, whereinthe change path for moving the robotic joints avoids interfering withthe refined path.
 35. The computer implemented method of claim 27,wherein the tool comprises a cutting tool for cutting the workpiece.